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Define the function $f\left(x\,y\right)$

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Context Panel: Assign Function


$f\left(x\,y\right)\=\frac{xy}{{x}^{4}plus;{y}^{4}}$$\stackrel{\text{assign as function}}{\to}$${f}$

Evaluate $\underset{x\to 0}{lim}f\left(x\,mx\right)$

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Calculus palette: Limit operator

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Context Panel: Simplify≻Assuming Positive


$\underset{x\to 0}{lim}f\left(x\,mx\right)$$\stackrel{\text{assuming positive}}{\to}$${\mathrm{\∞}}$



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Under the assumption that $m\>0$, the limit along any line through the origin does not exist because $f\left(x\,mx\right)$ becomes unbounded. Hence, the bivariate limit at the origin does not exist.
Alternatively, access Maple's bivariate limit through the Context Panel.
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Context Panel: Evaluate and Display Inline

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Context Panel: Limit (Bivariate)
(Fill in the Limit Point dialog as per Figure 3.2.7(a).)

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Figure 3.2.7(a) Limit Point dialog




$f\left(x\,y\right)$ = $\frac{{x}{}{y}}{{{x}}^{{4}}{\+}{{y}}^{{4}}}$$\stackrel{\text{bivariate limit}}{\to}$${\mathrm{undefined}}$${}$



Maple's declaration that the limit is undefined is equivalent to the more prevalent statement that the limit does not exist.
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